1. Field of the Invention
This invention relates to an apparatus and method for measuring characteristics of optical fibers in which characteristics in the longitudinal direction (distribution of polarization mode dispersion and distribution of magnitude of birefringence) of subject optical fibers are measured, and particularly to an apparatus and method for measuring characteristics of optical fibers that enable accurate measurement of characteristics of optical fibers.
2. Description of the Related Art
Recently, as higher transmission rates are increasingly demanded in the optical communication, transmission rates of 10 Gbps and 40 Gbps are getting realized. However, since dispersions such as material dispersion, waveguide dispersion, multimode dispersion and polarization mode dispersion exist in optical fibers as transmission media, waveform deterioration due to these dispersions is particularly considered to cause troubles. In the case where single-mode optical fibers are used, chromatic dispersion (sum of material dispersion and waveguide dispersion) and polarization mode dispersion are problems. Of these, chromatic dispersion can be compensated relatively easily by dispersion compensating fibers (DCF), reverse dispersion fibers (RDF) having the reverse characteristic of the chromatic dispersion of the single-mode optical fibers, a chromatic dispersion compensator or the like. Many solutions using these fibers or compensator are proposed and generally used.
On the other hand, polarization mode dispersion is caused by various elements such as structural defects of the optical fibers themselves, and elliptic deformation of the core, flexure, stress, and twisting due to manufacturing conditions, construction conditions, use environment and the like. These elements cause birefringence and polarization mode dispersion in the optical fibers. Polarization mode dispersion exists randomly in the optical fibers and changes largely. Therefore, it is difficult to compensate polarization mode dispersion using passive components.
Since compensation by passive components is difficult as described above, it is demanded that seriously defective parts of the already constructed optical fibers should be detected and removed and that defective parts should be detected in the manufacturing process to prevent entry into the markets or the results of measurement of polarization mode dispersion should be fed back to the manufacturing process to lower the proportion of defective parts when manufacturing optical fibers.
To realize detection of defective parts and the like, it is important to measure characteristics in the longitudinal direction of optical fibers and an optical fiber characteristics measuring apparatus is used. Particularly, an optical fiber characteristics measuring apparatus for measuring characteristics of polarization mode dispersion values is called polarization mode dispersion measuring apparatus. To measure this polarization mode dispersion, for example, optical components where polarization modes (polarization states) are orthogonal to each other can be transmitted by a predetermined distance and the time difference Δτ between the optical components generated by the transmission can be found.
A technique of measuring polarization mode dispersion will now be described with reference to FIG. 1. FIG. 1 shows the principle of the conventional measurement of polarization mode dispersion. In FIG. 1, an optical fiber 100 is, for example, a single-mode optical fiber and it is a subject optical fiber. Pulse light having angular frequencies ω1, ω2 (ω1≠ω2; these angular frequencies are slightly different) is inputted from one end (input side) of the optical fiber 100 and the pulse light transmitted through the optical fiber 100 is received at the other end (output side). On the input side, the pulse light is polarized in different polarization states (for example, 0° and 45° to a reference axis) and thus inputted to the optical fiber 100.
On the output side, the polarization state of the pulse light from the optical fiber 100 is divided into four directions (for example, 0°, 45°, 90°, and circular polarization) and the light intensity in each direction is detected. Stokes vector components (S0, S1, S2, and S3) are found from the light intensity in each direction. Generally, the transmission on the optical fiber 100 is expressed in the form of a Mueller matrix R (orthogonal matrix consisting of three row by three columns). Stokes vectors and Mueller matrix are expressed by the following equations.Ŝ=RŜ0
Ŝ,Ŝ0 represent Stokes vectors S,S0 
Since the light intensity of light inputted to the optical fiber 100 is already known, the Mueller matrix R can be found from the Stokes vector S0 of input light on the input side and the Stokes vector S of output light acquired on the output side. The Mueller matrix R is found for each of the angular frequencies ω1, ω2.
The Stokes vector S of the output light transmitted through the optical fiber 100 having birefringence is changed by the influence of polarization mode dispersion with respect to changes of the angular frequencies ω1, ω2 of the input light. This change is generally expressed by using a vector called polarization dispersion vector Ω within a polarization state space. The magnitude of the polarization dispersion vector Ω is equal to polarization mode dispersion. Therefore, the change in the polarization state of the output light based on the changes of the angular frequencies ω1, ω2 is expressed by the following known equation (1) using the polarization dispersion vector Ω and the Mueller matrix R. (See, for example, G. J. Foschini, C. D. Poole, “Statistical theory of polarization dispersion in single mode fibers,” JOURNAL OF LIGHTWAVE TECHNOLOGY, (U.S.), Laser & Electro-Optics Society (LEOS), November 1991, vol. 9, (No. 11), pp. 1439–1456.)
                                                                                          ⅆ                                      S                    ^                                                                    ⅆ                  ω                                            =                                                                                          ⅆ                      R                                                              ⅆ                      ω                                                        ⁢                                                            S                      ^                                        0                                                  =                                                                                                    ⅆ                        R                                                                    ⅆ                        ω                                                              ⁢                                          R                                              -                        1                                                              ⁢                                          S                      ^                                                        =                                                            Ω                      ⁢                                                                                          ⁢                                              S                        ^                                                              =                                                                  Ω                        ^                                            ×                                              S                        ^                                                                                                                  ⁢                                                  ⁢            wherein            ⁢                                                  ⁢                                          Ω                ^                            =                                                                                          [                                                                        Ω                          1                                                ⁢                                                                                                  ⁢                                                  Ω                          2                                                ⁢                                                                                                  ⁢                                                  Ω                          3                                                                    ]                                        T                                    ⁢                                                                          ⁢                  Ω                                =                                  (                                                                                    0                                                                                              -                                                      Ω                            3                                                                                                                                                Ω                          2                                                                                                                                                              Ω                          3                                                                                            0                                                                                              -                                                      Ω                            1                                                                                                                                                                                        -                                                      Ω                            2                                                                                                                                                Ω                          1                                                                                            0                                                                              )                                                              ⁢                                          ⁢                                    Ω              ^                        ⁢                                                  ⁢            represents            ⁢                                                  ⁢            polarization            ⁢                                                  ⁢            dispersion            ⁢                                                  ⁢            vector            ⁢                                                  ⁢            Ω            ⁢                                                  ⁢            and                    ⁢                                          ⁢                      Ω            ⁢                                                  ⁢            represents            ⁢                                                  ⁢            polarization            ⁢                                                  ⁢            dispersion            ⁢                                                  ⁢            matrix            ⁢                                                  ⁢                          Ω              .                                      ⁢                                                      (        1        )            
Ω1, Ω2 are linear polarization components that are different from each other. Ω3 is a circular polarization component. The Stokes vector S of the output light is a vector including four components (S0, S1, S2, S3) and the corresponding Mueller matrix R consists of four rows by four columns. However, the S0 component has all the power of the light including non-polarization components. For polarization mode dispersion, changes of light power can be ignored and changes of polarization components alone can be handled. Therefore, the Mueller matrix R is a matrix representing conversion of Stokes vectors in the case where polarization components are normalized and expressed in the form of Poincare' sphere. The Mueller matrix R thus consists of three rows by three columns, omitting the S0 component. Polarization mode dispersion is measured in the polarization state in independent four directions and the S0 component is deducted.
However, in the structure shown in FIG. 1, only polarization mode dispersion on the output end of the optical fiber 100 can be measured. Thus, unidirectional measurement using optical time domain reflectometry (hereinafter referred to as OTDR), which is a known technique, is used to measure the distribution in the longitudinal direction. (See, for example, JP-A-2003-106942, paragraphs No. 0024 to No. 0066 and FIGS. 1 to 9; JP-T-2000-510246 (the term “JP-T” as used herein means a published Japanese translation of a PCT application) and A. J. Rogers, “Polarization optical time domain reflectometry,” Electronics letters (U.K.), the Institution of Electrical Engineers (IEE), 1980, Vol. 16, No. 13, pp. 489–490.)
In this OTDR technique, short pulse light is inputted and back scattered light of this pulse light is measured, thereby measuring the characteristics of the optical fiber and also measuring the reflection position from the time taken for the back scattered light to return.
FIGS. 2 and 3 show structural views of a conventional optical fiber characteristics measuring apparatus. The same elements as those in FIG. 1 are denoted by the same symbols and numerals and will not be described further in detail. In FIGS. 2, and 3, a light source unit 10 has a tunable light source 11 and a pulse generator 12 and outputs pulse light with angular frequencies of ω1, ω2. The tunable light source 11 is a continuous light output unit. It variably controls the angular frequencies ω1, ω2 and outputs continuous light having the desired angular frequencies ω1, ω2. The pulse generator 12 converts the continuous light from the tunable light source 11 to pulse light having a desired pulse width and then outputs the pulse light.
A polarization controller 20 arbitrarily polarizes each pulse light from the light source unit 10 in a variable manner (into at least two different polarization states) and outputs the polarized light. A directional coupler 30 outputs the pulse light polarized by the polarization controller 20 to the optical fiber 100, and return light from the optical fiber 100, that is, back scattered light, is inputted to the directional coupler 30. A photodetector 40 detects the light intensity of the back scattered light from the directional coupler 30 in the polarization states of at least four directions synchronously with the pulse light outputted from the light source unit 10, and finds a normalized Stokes vector for each of the angular frequencies ω1, ω2.
An arithmetic operation unit 50 has a matrix calculating unit 51, a polarization dispersion vector calculating unit 52, a linear polarization calculating unit 53, and a dispersion value calculating unit 54. The arithmetic operation unit 50 calculates polarization dispersion vectors ΩB of the back scattered light on the basis of the Stokes vectors found by the photodetector 40, then calculates linear polarization components of the polarization dispersion vector Ω in a single direction by using the polarization dispersion vectors ΩB, and calculates polarization mode dispersion.
The matrix calculating unit 51 calculates a Mueller matrix from the normalized Stokes vector for each of the angular frequencies ω1, ω2. The polarization dispersion vector calculating unit 52 calculates the polarization dispersion vectors ΩB of the back scattered light at the angular frequencies from the Mueller matrix calculated by the matrix calculating unit 51. The linear polarization calculating unit 53 calculates the magnitude of linear polarization components (Ω1, Ω2) of the polarization dispersion vector Ω in a single direction from the polarization dispersion vectors ΩB of the back scattered light calculated by the polarization dispersion vector calculating unit 52. The dispersion value calculating unit 53 calculates a polarization mode dispersion value from the magnitude of the linear polarization components.
A control unit 60 designates the angular frequencies ω1, ω2, pulse width and pulse interval to the light source unit 10 and designates the polarization state to the polarization controller 20. The control unit 60 also designates the polarization state to be detected to the photodetector 40 and synchronizes the detection with the pulse light, and designates the calculation to the arithmetic operation unit 50.
The operation of this apparatus will now be described.
The control unit 60 causes the tunable light source 11 to output continuous light at the angular frequency ω1 and causes the pulse generator 12 to output pulse light with a desired pulse width at a desired pulse interval. Moreover, the control unit 60 causes the polarization controller 20 to output the pulse light with a polarization state of, for example, 0°, to the subject optical fiber 100 via the directional coupler 30.
Then, back scattered light, which is return light from the subject optical fiber 100, is inputted to the photodetector 40 via the directional coupler 30. The photodetector 40 detects the light intensity in four directions (for example, 0°, 45°, 90°, and circular polarization) in accordance with the designation from the control unit 60.
Similarly, the light intensities in four directions are detected with respect to the light at the angular frequency ω1 and in the polarization state of 45°, the light at the angular, frequency ω2 and in the polarization state of 0°, and the light at the angular frequency ω2 and in the polarization state of 45° in accordance with the designation from the control unit 60. The photodetector 40 then calculates a Stokes vector SB for each of the angular frequencies ω1, ω2.
As the Stokes vector SB is calculated, the control unit 60 instructs the arithmetic operation unit 50 to calculate polarization mode dispersion. In accordance with this instruction, the arithmetic operation unit 50 reads out the Stokes vector SB from the photodetector 40 and the matrix calculating unit 51 calculates a Mueller matrix RB of the back scattered light from the Stokes vector SB.
The polarization dispersion vector calculating unit 52 calculates polarization dispersion vectors ΩB of the back scattered light from the Mueller matrix RB. That is, when the light intensity of the back scattered light from the subject optical fiber 100 is measured, the relation of the following equation (2) based on the Mueller matrix RB and Stokes vector SB holds, similarly to the equation (1).
                                                                        ⅆ                                                      S                    ^                                    B                                                            ⅆ                ω                                      =                                                            ⅆ                                      R                    B                                                                    ⅆ                  ω                                            ⁢                              R                B                                  -                  1                                            ⁢                                                S                  ^                                B                                              ⁢                                          ⁢                                                                      S                  ^                                B                            ⁢                                                          ⁢              represents              ⁢                                                          ⁢              Stokes              ⁢                                                          ⁢              vector              ⁢                                                          ⁢                              S                B                            ⁢                                                          ⁢              of              ⁢                                                          ⁢              back              ⁢                                                          ⁢              scattered              ⁢                                                          ⁢              light                        ,                                                  ⁢            and                    ⁢                                          ⁢                                    R              B                        ⁢                                                  ⁢            represents            ⁢                                                  ⁢            Mueller            ⁢                                                  ⁢            matrix            ⁢                                                  ⁢                          R              B                        ⁢                                                  ⁢            of            ⁢                                                  ⁢            back            ⁢                                                  ⁢            scattered            ⁢                                                  ⁢                          light              .                                      ⁢                                                      (        2        )            
As the polarization dispersion matrix ΩB representing the polarization dispersion vectors ΩB of the back scattered light, the following equation (3) can be acquired from the equations (1) and (2).
                                                                        Ω                ^                            B                        =                                                            ⅆ                                      R                    B                                                                    ⅆ                  ω                                            ⁢                              R                B                                  -                  1                                                              ⁢                                          ⁢                                                                      Ω                  ^                                ⁢                                                                                              B                ⁢                                                                                        ⁢                                                  ⁢            represents            ⁢                                                  ⁢            polarization            ⁢                                                  ⁢            dispersion            ⁢                                                  ⁢            vectors            ⁢                                                  ⁢                                          Ω                B                            .                                      ⁢                                                      (        3        )            
In this manner, the polarization dispersion vector calculating unit 52 calculates the polarization dispersion vectors ΩB.
Moreover, the linear polarization calculating unit 53 calculates the magnitude of linear polarization components of the polarization dispersion vector Ω in a single direction. That is, it is generally known that the relation between the Mueller matrix R and the Mueller matrix RB of the back scattered light is expressed by the following equation (4) using a matrix M.
                              R          B                =                              MR            T                    ⁢                      MR            ⁢                                                  (                          M              =                              (                                                                            1                                                              0                                                              0                                                                                                  0                                                              1                                                              0                                                                                                  0                                                              0                                                                                      -                        1                                                                                            )                                      )                                              (        4        )            
Therefore, as the equation (4) is substituted into the equation (3), the polarization dispersion vector ΩB of the back scattered light, the Mueller matrix R in the single direction, and the linear polarization component ΩL of the polarization dispersion vector Ω in the single direction are in the relation of the following equation (5){circumflex over (Ω)}B=2MRT{circumflex over (Ω)}L  (5)
({circumflex over (Ω)}L=[Ω1 Ω2 0 ]T)
{circumflex over (Ω)}L represents linear polarization component vector ΩL.
In the case of calculating the magnitude (ΔτB) of the polarization dispersion vector Ω8 of the back scattered light, the magnitude of the vector converted by MR (transported matrix) on the right side of the equation (5) is not changed because the matrix M and the Mueller matrix R are orthogonal matrices. Therefore, the following equation holds.ΔτB=|{circumflex over (Ω)}B|=2√{square root over (Ω12+Ω22)}
In this manner, the linear polarization calculating unit 53 calculates the magnitude of the linear polarization components (Ω1, Ω2) of the polarization dispersion vector Ω in the single direction. On the statistical assumption of Gaussian distribution as the distribution of the components Ω1 to Ω3 of the polarization dispersion vector Ω, the relation between the magnitude (ΔτB) of the polarization dispersion vector ΩB of the back scattered light and the magnitude (Δτ) of the polarization dispersion vector Ω of polarization mode dispersion to be found is expressed by the following equation.
      〈          Δ      ⁢                          ⁢      τ        〉    =            〈              Δτ        B            〉        ⁢          2      π      
<ΔτB> is a statistical average value of values that are measured many times under various conditions.
Therefore, the dispersion value calculating unit 54 calculates the value of polarization mode dispersion from the polarization dispersion vector ΩB acquired from the back scattered light. (See, for example, Fabrizio Corsi, Andrea Galtarossa, Luca Palmieri, “Polarization Mode Dispersion Characterization of Single-Mode Optical Fiber Using Backscattering Technique,” JOURNAL OF LIGHTWAVE TECHNOLOGY (U.S.), Laser & Electro-Optics Society (LEOS), October 1998, Vol. 16, No. 10, pp. 1832–1843.)
In this manner, the magnitude (ΔτB) of the polarization dispersion vector ΩB of pulse light of two wavelengths (angular frequencies ω1, ω2) is calculated and polarization mode dispersion (Δτ) is measured.
However, the apparatus shown in FIGS. 2 and 3 has a problem that it cannot detect the circular polarization component of birefringence within the subject optical fiber 100 simply and directly, as described in J. N. Ross, “Birefringence measurement in optical fibers by polarization-optical time-domain reflectometry,” Applied Optics (U.S.), Optical Society of America (OSA), October 1982, Vol. 21, No. 19, pp. 3489–3495. As is clear from the equation (5), only the effect of the linear polarization components (Ω1, Ω2) is left and the effect of the circular polarization component Ω3 is eliminated. Therefore, when the magnitude (ΔτB) of the polarization dispersion vector ΩB of the back scattered light is compared with the polarization mode dispersion (Δτ), the following formula holds.ΔτB=2√{square root over (Ω12+Ω22)}<2√{square root over (Ω12+Ω22+Ω32)}=2Δτ
Of course, the polarization dispersion vector ΩB acquired from the back scattered light only includes the linear polarization components (Ω1, Ω2) of the polarization dispersion vector Ω in the single direction. The OTDR technique measures the light entered and returning from the subject optical fiber 100. If Δτ=ΔτB/2 is simply assumed, polarization mode dispersion Δτ cannot be calculated accurately. For example, if the circular polarization component Ω3 increases because of torsion of the subject optical fiber 100 or the like, there is a possibility that polarization mode dispersion (Δτ) takes a relatively small value.
Generally, the average magnitude <ΔτB> of the polarization dispersion vectors acquired from the back scattered light is multiplied by 0.64 (which is approximately 2/π), as shown in the above-described equation. However, since this value is acquired from many numerical simulations and statistics, the value is not effective for all the subject optical fibers 100 and it is difficult to accurately find polarization mode dispersion, that is, the characteristics of the optical fibers